We have a function:
y = 1 + sin x.
Let us find the angle of inclination of the tangent to the graph of the function with the abscissa at the point x0 = A.
The angle of inclination of the tangent to the graph of the function is found from its equation. Let’s write it down:
y = y ‘(x0) * (x – x0) + y (x0).
The angle of inclination is found as follows – its tangent is equal to the slope of a straight line, and in turn, the slope of a straight line is a factor in the variable, that is, y ‘(x0). Let’s find him.
y ‘(x) = cos x;
y ‘(x0) = cos П = -1.
A = arctan (-1) = 135 °.
The angle of inclination of the tangent is 135 °.
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